﻿{
 "cells": [
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   "metadata": {},
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   "source": [
    "# 逻辑回归\n",
    "\n",
    "## 🧠 一、逻辑回归到底是什么？\n",
    "\n",
    "逻辑回归是一种用于 **二分类**（也可以扩展到多分类）的问题的 **监督学习模型**。尽管名字叫“回归”，但它其实是一个**分类算法**。\n",
    "\n",
    "> **用途：** 用来预测一个样本属于某个类别的概率，例如：\n",
    "> - 邮件是否是垃圾邮件？\n",
    "> - 一个人是否会点击广告？\n",
    "> - 病人是否患病？\n",
    "\n",
    "---\n",
    "\n",
    "## ⚙️ 二、逻辑回归的数学原理\n",
    "\n",
    "### ✅ 1. 假设函数（sigmoid 函数）\n",
    "\n",
    "逻辑回归不是直接预测 $ y $，而是预测它为正类的概率：\n",
    "\n",
    "$$\n",
    "P(y=1 \\mid x) = \\sigma(z) = \\frac{1}{1 + e^{-z}}, \\quad z = \\theta^T x\n",
    "$$\n",
    "\n",
    "其中：\n",
    "\n",
    "- $ x $：特征向量\n",
    "- $ \\theta $：模型参数\n",
    "- $ \\sigma(z) $：**sigmoid 函数**，把任意实数压缩到 (0,1) 区间\n",
    "\n",
    "> 直观理解：sigmoid 像一个 S 型函数，可以把线性模型输出转换成“概率感”。\n",
    "\n",
    "---\n",
    "\n",
    "### ✅ 2. 决策边界\n",
    "\n",
    "预测时，如果：\n",
    "\n",
    "$$\n",
    "P(y=1 \\mid x) \\geq 0.5 \\Rightarrow \\text{预测为正类}\n",
    "$$\n",
    "$$\n",
    "P(y=1 \\mid x) < 0.5 \\Rightarrow \\text{预测为负类}\n",
    "$$\n",
    "\n",
    "所以 $ \\theta^T x = 0 $ 就是分类的“分界线”（或者超平面） → **决策边界**\n",
    "\n",
    "---\n",
    "\n",
    "### ✅ 3. 损失函数（交叉熵）\n",
    "\n",
    "逻辑回归的损失函数不是 MSE，而是**对数似然损失**（也叫交叉熵损失）：\n",
    "\n",
    "$$\n",
    "J(\\theta) = -\\frac{1}{n} \\sum_{i=1}^{n} \\left[ y^{(i)} \\log(\\hat{y}^{(i)}) + (1 - y^{(i)}) \\log(1 - \\hat{y}^{(i)}) \\right]\n",
    "$$\n",
    "\n",
    "其中：\n",
    "\n",
    "- $ \\hat{y}^{(i)} = \\sigma(\\theta^T x^{(i)}) $\n",
    "- 目标是最小化 $ J(\\theta) $\n",
    "\n",
    "这个函数是 **凸函数**，所以可以用梯度下降求解。\n",
    "\n",
    "---\n",
    "\n",
    "## 🔢 三、逻辑回归训练过程\n",
    "\n",
    "1. 初始化参数 $ \\theta $\n",
    "2. 通过训练集计算预测值 $ \\hat{y} $\n",
    "3. 使用交叉熵计算损失\n",
    "4. 使用梯度下降（或其他优化方法）更新参数\n",
    "5. 重复迭代直到收敛\n",
    "\n",
    "---\n",
    "\n",
    "## 📈 四、逻辑回归的优点\n",
    "\n",
    "✅ 简单、可解释性强\n",
    "✅ 训练速度快\n",
    "✅ 可以输出概率\n",
    "✅ 对线性可分数据效果好\n",
    "✅ 可扩展到多分类（One-vs-Rest）\n",
    "\n",
    "---\n",
    "\n",
    "## 🧱 五、常见限制\n",
    "\n",
    "❌ 无法处理非线性决策边界（除非加特征变换）\n",
    "❌ 对离群值敏感\n",
    "❌ 需要特征标准化以加速收敛\n",
    "\n",
    "---\n",
    "\n",
    "## 🧠 如果用一句话总结逻辑回归：\n",
    "\n",
    "> **逻辑回归是一种使用 sigmoid 函数将线性模型输出映射为概率的二分类模型，训练过程使用交叉熵损失，通过梯度下降拟合最优参数。**"
   ],
   "id": "3d29e5e21bbb54fe"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-04-24T15:56:27.712252Z",
     "start_time": "2025-04-24T15:56:27.702906Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "# 加载数据\n",
    "iris = load_iris()\n",
    "X = iris.data\n",
    "y = iris.target\n",
    "target_names = iris.target_names\n",
    "\n",
    "# 只取前两类（setosa 和 versicolor），以及前两个特征（sepal length, sepal width）\n",
    "X = X[y != 2, :2]\n",
    "y = y[y != 2]\n",
    "\n",
    "# 标准化\n",
    "scaler = StandardScaler()\n",
    "X_std = scaler.fit_transform(X)"
   ],
   "id": "b89e61ba17d54cd6",
   "outputs": [],
   "execution_count": 2
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "# 数据集介绍\n",
    "\n",
    "```shell\n",
    "1. Title: Iris Plants Database\n",
    "\tUpdated Sept 21 by C.Blake - Added discrepency information\n",
    "\n",
    "2. Sources:\n",
    "     (a) Creator: R.A. Fisher\n",
    "     (b) Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\n",
    "     (c) Date: July, 1988\n",
    "\n",
    "3. Past Usage:\n",
    "   - Publications: too many to mention!!!  Here are a few.\n",
    "   1. Fisher,R.A. \"The use of multiple measurements in taxonomic problems\"\n",
    "      Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions\n",
    "      to Mathematical Statistics\" (John Wiley, NY, 1950).\n",
    "   2. Duda,R.O., & Hart,P.E. (1973) Pattern Classification and Scene Analysis.\n",
    "      (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.\n",
    "   3. Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\n",
    "      Structure and Classification Rule for Recognition in Partially Exposed\n",
    "      Environments\".  IEEE Transactions on Pattern Analysis and Machine\n",
    "      Intelligence, Vol. PAMI-2, No. 1, 67-71.\n",
    "      -- Results:\n",
    "         -- very low misclassification rates (0% for the setosa class)\n",
    "   4. Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\".  IEEE\n",
    "      Transactions on Information Theory, May 1972, 431-433.\n",
    "      -- Results:\n",
    "         -- very low misclassification rates again\n",
    "   5. See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al's AUTOCLASS II\n",
    "      conceptual clustering system finds 3 classes in the data.\n",
    "\n",
    "4. Relevant Information:\n",
    "   --- This is perhaps the best known database to be found in the pattern\n",
    "       recognition literature.  Fisher's paper is a classic in the field\n",
    "       and is referenced frequently to this day.  (See Duda & Hart, for\n",
    "       example.)  The data set contains 3 classes of 50 instances each,\n",
    "       where each class refers to a type of iris plant.  One class is\n",
    "       linearly separable from the other 2; the latter are NOT linearly\n",
    "       separable from each other.\n",
    "   --- Predicted attribute: class of iris plant.\n",
    "   --- This is an exceedingly simple domain.\n",
    "   --- This data differs from the data presented in Fishers article\n",
    "\t(identified by Steve Chadwick,  spchadwick@espeedaz.net )\n",
    "\tThe 35th sample should be: 4.9,3.1,1.5,0.2,\"Iris-setosa\"\n",
    "\twhere the error is in the fourth feature.\n",
    "\tThe 38th sample: 4.9,3.6,1.4,0.1,\"Iris-setosa\"\n",
    "\twhere the errors are in the second and third features.\n",
    "\n",
    "5. Number of Instances: 150 (50 in each of three classes)\n",
    "\n",
    "6. Number of Attributes: 4 numeric, predictive attributes and the class\n",
    "\n",
    "7. Attribute Information:\n",
    "   1. sepal length in cm\n",
    "   2. sepal width in cm\n",
    "   3. petal length in cm\n",
    "   4. petal width in cm\n",
    "   5. class:\n",
    "      -- Iris Setosa\n",
    "      -- Iris Versicolour\n",
    "      -- Iris Virginica\n",
    "\n",
    "8. Missing Attribute Values: None\n",
    "\n",
    "Summary Statistics:\n",
    "\t         Min  Max   Mean    SD   Class Correlation\n",
    "   sepal length: 4.3  7.9   5.84  0.83    0.7826\n",
    "    sepal width: 2.0  4.4   3.05  0.43   -0.4194\n",
    "   petal length: 1.0  6.9   3.76  1.76    0.9490  (high!)\n",
    "    petal width: 0.1  2.5   1.20  0.76    0.9565  (high!)\n",
    "\n",
    "9. Class Distribution: 33.3% for each of 3 classes.\n",
    "\n",
    "```"
   ],
   "id": "1a034d32f6636359"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-04-24T15:56:50.560615Z",
     "start_time": "2025-04-24T15:56:50.322872Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 训练逻辑回归模型\n",
    "clf = LogisticRegression()\n",
    "clf.fit(X_std, y)\n",
    "\n",
    "# 可视化决策边界\n",
    "def plot_decision_boundary(model, X, y):\n",
    "    x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5\n",
    "    y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5\n",
    "    h = 0.01  # 网格粒度\n",
    "    xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n",
    "                         np.arange(y_min, y_max, h))\n",
    "    Z = model.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "    Z = Z.reshape(xx.shape)\n",
    "\n",
    "    plt.figure(figsize=(8, 6))\n",
    "    plt.contourf(xx, yy, Z, cmap=plt.cm.Pastel2, alpha=0.8)\n",
    "    plt.scatter(X[:, 0], X[:, 1], c=y, edgecolors='k', cmap=plt.cm.Set1)\n",
    "    plt.xlabel('Sepal length (standardized)')\n",
    "    plt.ylabel('Sepal width (standardized)')\n",
    "    plt.title('Logistic Regression on Iris (Setosa vs Versicolor)')\n",
    "    plt.grid(True)\n",
    "    plt.show()\n",
    "\n",
    "# 绘图\n",
    "plot_decision_boundary(clf, X_std, y)"
   ],
   "id": "4328edf7c6d08679",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 3
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# 三分类",
   "id": "4d1f49894262412f"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-04-24T15:58:10.342473Z",
     "start_time": "2025-04-24T15:58:10.142842Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "# 加载数据\n",
    "iris = load_iris()\n",
    "X = iris.data[:, :2]  # 只取前两个特征用于可视化\n",
    "y = iris.target\n",
    "target_names = iris.target_names\n",
    "\n",
    "# 标准化\n",
    "scaler = StandardScaler()\n",
    "X_std = scaler.fit_transform(X)\n",
    "\n",
    "# 多分类逻辑回归训练\n",
    "clf = LogisticRegression(solver='lbfgs')\n",
    "clf.fit(X_std, y)\n",
    "\n",
    "# 绘制决策边界函数\n",
    "def plot_multiclass_decision_boundary(model, X, y, target_names):\n",
    "    x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5\n",
    "    y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5\n",
    "    h = 0.01  # 网格粒度\n",
    "    xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n",
    "                         np.arange(y_min, y_max, h))\n",
    "    Z = model.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "    Z = Z.reshape(xx.shape)\n",
    "\n",
    "    plt.figure(figsize=(8, 6))\n",
    "    plt.contourf(xx, yy, Z, cmap=plt.cm.Pastel1, alpha=0.8)\n",
    "    scatter = plt.scatter(X[:, 0], X[:, 1], c=y, edgecolors='k', cmap=plt.cm.Set1)\n",
    "    plt.xlabel('Sepal length (standardized)')\n",
    "    plt.ylabel('Sepal width (standardized)')\n",
    "    plt.title('Multiclass Logistic Regression on Iris')\n",
    "    plt.grid(True)\n",
    "    # 添加图例\n",
    "    handles, _ = scatter.legend_elements()\n",
    "    plt.legend(handles, target_names, title=\"Classes\")\n",
    "    plt.show()\n",
    "\n",
    "# 绘图\n",
    "plot_multiclass_decision_boundary(clf, X_std, y, target_names)\n"
   ],
   "id": "53473da571ca4f27",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 4
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "## 逻辑回归优化算法\n",
    "\n",
    "在 `scikit-learn` 中，`LogisticRegression` 类支持多种优化算法，这些算法用于求解逻辑回归模型的参数。以下是一些常用的优化算法及其特点：\n",
    "\n",
    "### 1. **liblinear**\n",
    "- **描述**：这是一个用于小型数据集的优化器，使用坐标下降法。\n",
    "- **优点**：\n",
    "  - 适合小型数据集和二分类问题。\n",
    "  - 可以处理L1和L2正则化。\n",
    "- **缺点**：\n",
    "  - 对于大规模数据集，速度较慢。\n",
    "\n",
    "### 2. **newton-cg**\n",
    "- **描述**：使用牛顿法（Newton's method）和共轭梯度法（Conjugate Gradient）来优化。\n",
    "- **优点**：\n",
    "  - 对于中型数据集，收敛速度较快。\n",
    "  - 适合L2正则化。\n",
    "- **缺点**：\n",
    "  - 内存消耗较高，不适合非常大的数据集。\n",
    "\n",
    "### 3. **lbfgs**\n",
    "- **描述**：使用L-BFGS（Limited-memory Broyden-Fletcher-Goldfarb-Shanno）算法，这是牛顿法的一种变体，适用于大规模数据集。\n",
    "- **优点**：\n",
    "  - 内存效率高，适合大规模数据集。\n",
    "  - 收敛速度快，通常表现良好。\n",
    "- **缺点**：\n",
    "  - 对于非常稀疏的数据，可能不如其他方法效果好。\n",
    "\n",
    "### 4. **sag**\n",
    "- **描述**：使用随机平均梯度下降（Stochastic Average Gradient）算法。\n",
    "- **优点**：\n",
    "  - 对于大规模数据集，收敛速度快。\n",
    "  - 可以处理L2正则化。\n",
    "- **缺点**：\n",
    "  - 需要数据集为稠密格式（dense format）。\n",
    "\n",
    "### 5. **saga**\n",
    "- **描述**：这是对SAG算法的扩展，支持L1正则化。\n",
    "- **优点**：\n",
    "  - 适用于大规模数据集，能够处理L1和L2正则化。\n",
    "  - 收敛速度较快，适合稀疏数据。\n",
    "- **缺点**：\n",
    "  - 计算复杂度相对较高。"
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    "# N(N>2)分类的原理\n",
    "\n",
    "逻辑回归（Logistic Regression）本质上是一个二分类算法，但可以通过以下三种策略扩展到三分类及多分类问题：\n",
    "\n",
    "---\n",
    "\n",
    "1. **一对多（One-vs-Rest, OvR）**\n",
    "\n",
    "    原理：\n",
    "    为每个类别训练一个独立的二分类器，判断样本是否属于该类别（是/否）。\n",
    "\n",
    "    实现步骤：\n",
    "    1. 假设有 $ K $ 个类别，训练 $ K $ 个二分类逻辑回归模型。\n",
    "    2. 第 $ i $ 个模型将第 $ i $ 类作为正类，其余所有类作为负类。\n",
    "    3. 预测时，选择概率最高的模型对应的类别。\n",
    "\n",
    "    示例（三分类：A/B/C类）：\n",
    "    + 模型1：A vs (B+C)\n",
    "    + 模型2：B vs (A+C)\n",
    "    + 模型3：C vs (A+B)\n",
    "    + 最终预测：`argmax(模型1概率, 模型2概率, 模型3概率)`\n",
    "\n",
    "    特点：\n",
    "\n",
    "    + 简单高效，适合类别较少的情况。\n",
    "    + 可能因类别不平衡导致某些分类器性能下降。\n",
    "    ---\n",
    "\n",
    "2. **一对一（One-vs-One, OvO）**\n",
    "\n",
    "    原理：\n",
    "    为每对类别训练一个二分类器，通过投票决定最终类别。\n",
    "\n",
    "    实现步骤：\n",
    "    1. 对 $ K $ 个类别，训练 $ \\frac{K(K-1)}{2} $ 个二分类器（如三分类需3个模型）。\n",
    "    2. 每个模型只区分一对类别（如A vs B，A vs C，B vs C）。\n",
    "    3. 预测时，所有模型投票，得票最多的类别胜出。\n",
    "\n",
    "    示例（三分类）：\n",
    "    + 模型1：A vs B\n",
    "    + 模型2：A vs C\n",
    "    + 模型3：B vs C\n",
    "    + 若模型1预测A，模型2预测A，模型3预测B → 最终预测A（2票）。\n",
    "\n",
    "    特点：\n",
    "\n",
    "    + 训练更多模型，但每个模型只需部分数据。\n",
    "    + 适合类别数较多时（如SVM常采用此方法）。\n",
    "    ---\n",
    "\n",
    "3. **多项式逻辑回归（Softmax回归）**\n",
    "\n",
    "    原理：\n",
    "    直接扩展逻辑回归，使用Softmax函数输出多类概率分布。\n",
    "\n",
    "    数学形式：\n",
    "    $$\n",
    "    P(y=i \\mid \\mathbf{x}) = \\frac{e^{\\mathbf{w}_i^T \\mathbf{x}}}{\\sum_{j=1}^K e^{\\mathbf{w}_j^T \\mathbf{x}}}\n",
    "    $$\n",
    "    其中 $ \\mathbf{w}_i $ 是第 $ i $ 类的权重向量。\n",
    "\n",
    "    特点：\n",
    "\n",
    "    + 直接建模多分类问题，无需训练多个模型。\n",
    "    + 输出概率归一化，适合互斥类别。\n",
    "    + 计算成本较高（需优化所有类的权重）。\n",
    "---\n",
    "\n",
    "对比总结\n",
    "| 方法         | 训练模型数   | 适用场景               | 优缺点                     |\n",
    "|------------------|------------------|---------------------------|-------------------------------|\n",
    "| OvR          | $ K $          | 类别较少（<10）            | 简单，但可能类别不平衡         |\n",
    "| OvO          | $ K(K-1)/2 $   | 类别较多或数据分布复杂      | 训练成本高，但每个模型更精准   |\n",
    "| Softmax      | 1个综合模型      | 类别互斥且特征共享         | 直接多分类，但需更多计算资源   |"
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